Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
In this chapter, Fourier series is introduced for functions which are Riemann integrable and are of bounded exponential growth. Orthogonal relations; least square error, completeness relation and Riemann- Lebesgue theorem are also considered. The Fourier series is applied to obtain a series solution to some periodic boundary value problems. Also provided are Maple examples for applications of Fourier series to ordinary differential equations.
Keywords:
Bounded exponential growth, Boundary value problems, Completeness relation, Differential equations, Fourier series, Least square error, Periodic solutions, Riemann- Lebesgue theorem
We recommend
Authors:Bentham Science Books